Related papers: Incompatibility of Observables as State-Independen…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary…
Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not…
The Heisenberg uncertainty principle imposes a fundamental restriction in quantum mechanics, stipulating that measuring one observable completely erases the information on its conjugate one, thereby preventing simultaneous measurements of…
One of the central features of quantum theory is that there are pairs of quantum observables that cannot be measured simultaneously. This incompatibility of quantum observables is a necessary ingredient in several quantum phenomena, such as…
We investigate entropic uncertainty relations for two or more binary measurements, for example spin-$\frac{1}{2}$ or polarisation measurements. We argue that the effective anti-commutators of these measurements, i.e. the anti-commutators…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…
We investigate the role of symmetric quantum cloning machines (QCMs) in quantifying the mutual incompatibility of quantum observables. Specifically, we identify a cloning-based incompatibility measure whereby the incompatibility of a set of…
Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet…
We study a possible improvement of uncertainty relations. The Heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables. The Schroedinger uncertainty…
Quantum incompatibility, referred as the phenomenon that some quantum measurements cannot be performed simultaneously, is necessary for various quantum information processing tasks, such as nonlocality and steering. When these applications…
The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…
We introduce a new way of quantifying the degrees of incompatibility of two ob- servables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all…
Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually…
An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for…